Introduction. Modeling snow load in a probabilistic context is a complex scientific and technical challenge due to limited statistical information, regional characteristics, and a significant coefficient of variation reaching 95 %. To ensure the reliability of structural objects, accurate snow load models are required, which can be used to predict the maximum snow load over the estimated service life of the structure.

Aim. The research is aimed at developing a probabilistic algorithm for obtaining a statistical sample of data on the weight of snow height in an arbitrary location based on the method of co-kriging and processing data from annual meteorological observations.

Materials and methods. The article proposes using the co-kriging method for spatial interpolation of snow load on the ground based on available weather station data to obtain a statistical sample of data over 50 years in arbitrary geographic coordinates across the Russian Federation. Snow load on the ground is estimated based on the water content of the snow. The resulting statistical data are approximated by a Gumbel probability distribution for further reliability analysis, or a nonparametric 0.98-quantile estimate is performed for semi-probabilistic structural design.

Results. Statistical data from meteorological stations on snow water content over a 50-year period are analyzed, and a visualization of parameter variability is provided, reflecting the

significant variability of snow cover weight and statistical parameters. The proposed algorithm for generating a stochastic snow load on the ground model based on co-kriging demonstrated good convergence during cross-validation with actual values – a 2 % difference compared to the second maximum over 50 years and a 5 % difference in the Gumbel distribution center parameter. Nonparametric approaches, such as the bootstrap method, can be used to estimate only the required quantile (e.g., the 0.98th quantile), allowing for a quantile estimate to be obtained as a confidence interval. An algorithm for constructing a distribution function of snow load on the ground maxima over a period of n years, taking into account climate trends, is proposed based on statistical data simulation.

Conclusions. The proposed approach to snow load on the ground modeling allows for statistical data estimation at any given point for subsequent full probabilistic design of a structural object. Given established trends – both downward and upward – the proposed model can be used to estimate the probability of failure of a structure over a specified period of operation. The conversion from snow load on the ground to snow load on the roof is accomplished through coefficients, which are also random in nature and require probabilistic analysis, as provided in the JCSS probabilistic standard. Additionally, the proposed approach can be used to investigate locations with the greatest data interpolation errors, where additional statistical observations of snow weight are required to generate more accurate stochastic snow load models.  

Introduction. Structural reliability is one of the key parameters of a building at all stages of its life cycle. An effective approach to reliability analysis is the use of probabilistic methods of structural mechanics. The actual problem of their application in practice is incomplete statistical information about the design parameters.

Aim. The research is aimed at developing a probabilistic approach to analyzing the reliability of structural elements in conditions of incomplete statistical information on random variables using methods for probability distribution function recovery.

Materials and methods. Nonparametric methods are used to recover an unknown probability distribution density of random variables based on data from a sample. Due to the fact that the reconstructed probability densities function has a complex analytical form for generating data using the N.V. Smirnov’s inverse transform sampling, the study uses the method of acceptance-rejection sampling (A/R sampling) for further use of the Monte Carlo Simulation (MCS) in the problem of probabilistic reliability analysis.

Results. The proposed algorithm is demonstrated by the example of a probabilistic calculation of the reliability of an element of a rod system. In case of incomplete statistical information, individual design parameters are estimated as confidence intervals, which leads to an interval estimate of the failure probability for a structural element. The estimated reliability is taken at the upper limit of the failure probability interval within the safety level.

Conclusions. The numerical approach to assessing the reliability of a structural object or its individual element is presented for cases of incomplete statistical information, in which reliability is expressed as an interval of failure probability. If the failure probability interval turns out to be too wide to make a decision on the reliability level, it can be narrowed by additional collection of statistical data on random parameters, or the cross-section can be increased (at the design stage) or reinforcement (at the operational stage) of the structural element can be performed. 

The article describes a problem of uncertainty modeling of statistical data in the problems of structural reliability analysis. There are elements of subjectivity in decisions making about the type of distribution of a random variable and its parameters on the analysis of the results of numerical experiments and real tests of control samples of steel on yield strength. As an alternative to the cumulative distribution function it is proposed to use p-box as a model of a random variable. The new type of a p-box is proposed on the basis of the Dvoretzky–Kiefer–Wolfowitz inequality, which allows to form the area of possible cumulative distribution functions without base on classical probability distributions. By the example of reliability analysis of a steel structural element, the variants of using different p-boxes are shown depending on the available statistical data. The probability of no-failure is presented in interval form based on p-boxes. If the result of reliability analysis by the lower boundary does not allow to make a decision about the safety level of a structural element, two options are possible: to reduce the uncertainty of the data by conducting additional statistical researches or to increase the cross-sectional area of the structural element.  

The article presents an approach to evaluation the reliability index of steel truss bars with the uncertainty of random variables expressed in the presence of information only about the bounds of variability. Different methods of estimating the bounds of variability for random variables are presented. The new approach is also developed using the provisions of the theory of possibility and the Dvoretzky–Kiefer–Wolfowitz inequality (DKW). The reliability index allows to compare various design solutions by the safety criterion, identify structural elements with the highest failure probability for monitoring the technical state and to quantify the increase in the safety level with strengthening of structural elements. The Monte Carlo statistical simulation data reflect the analogy of the non-probabilistic reliability index in the considered approach with the non-failure probability of the truss bar.